Envy divides society

June 17, 2020

It's generally recognized that differences in background and education cement class differences. It is less clear when and under what circumstances individual psychological forces can drive an initially homogenous social group apart and ultimately divide it. Claudius Gros, professor for theoretical physics at Goethe University, investigated this question in a mathematical precise way using game theory methods. "In the study, societies of agents - acting individuals - are simulated within game theory, which means that everybody optimises her/his success according to predetermined rules. I wanted to find out whether social differences can emerge on their own if no one starts off with advantages - that is, when all actors have the same skills and opportunity," the physicist explains.

The study is based on the assumption that there are things in every society that are coveted but limited - such as jobs, social contacts and positions of power. An inequality is created if the top position is already occupied and someone must therefore accept the second-best job - but not, however, a societal division. With the help of mathematical calculations Gros was able to demonstrate that envy, which arises from the need to compare oneself with others, alters individual behaviour and consequently the agents' strategies in characteristic ways. As a result of this changed behaviour, two strictly separate social classes arise.

Game theory provides the mathematical tools necessary for the modelling of decision situations with several participants, as in Gros' study. In general, constellations in which the decision strategies of the individual actors mutually influence each other are particularly revealing. The success of the individual depends then not only on his or her own actions, but on others' actions as well, which is typical of both economic and social contexts. Game theory is consequently firmly anchored in the economy. The stability condition of game theory, the "Nash equilibrium", is a concept developed by John Forbes Nash in his dissertation in 1950, using the example of poker players. It states that in equilibrium no player has anything to gain by changing their strategy if the other players do not change theirs either. An individual only tries out new behaviour patterns if there is a potential gain. Since this causal chain also applies to evolutionary processes, the evolutionary and behavioural sciences regularly fall back on game theoretical models, for example when researching animal behaviours such as the migratory flight routes of birds, or their competition for nesting sites.

Even in an envy-induced class society there is no incentive for an individual to change his or her strategy, according to Gros. It is therefore Nash stable. In the divided envy society there is a marked difference in income between the upper and lower class which is the same for all members of each social class. Typical for the members of the lower class is, according to Gros, that they spend their time on a series of different activities, something game theory terms a "mixed strategy". Members of the upper class, however, concentrate on a single task, i.e., they pursue a "pure strategy". It is also striking that the upper class can choose between various options while the lower class only has access to a single mixed strategy. "The upper class is therefore individualistic, while agents in the lower class are lost in the crowd, so to speak," the physicist sums up.

In Claudius Gros' model, whether an agent lands in the upper or lower class is ultimately a matter of coincidence. It is decided by the dynamics of competition, and not by origin. For his study, Gros developed a new game theoretical model, the "shopping trouble model" and worked out a precise analytical solution. From it, he derives that an envy-induced class society possesses characteristics that are deemed universal in the theory of complex systems. The result is that the class society is beyond political control to a certain degree. Political decision-makers lose a portion of their options for control when society spontaneously splits into social classes. In addition, Gros' model demonstrates that envy has a stronger effect when the competition for limited resources is stronger. "This game theoretical insight could be of central significance. Even an 'ideal society' cannot be stably maintained in the long term - which ultimately makes the striving for a communistic society seem unrealistic," the scientist remarks.
-end-
Publication: Claudius Gros, Self induced class stratification in competitive societies of agents: Nash stability in the presence of envy, Royal Society Open Science, Vol 7, 200411 (2020). Link: https://royalsocietypublishing.org/doi/10.1098/rsos.200411

Further information: Professor Claudius Gros, Institute for Theoretical Physics, Riedberg Campus, E-Mail gros07@itp.uni-frankfurt.de

Current news about science, teaching, and society can be found on GOETHE-UNI online

Goethe University is a research-oriented university in the European financial centre Frankfurt am Main. The university was founded in 1914 through private funding, primarily from Jewish sponsors, and has since produced pioneering achievements in the areas of social sciences, sociology and economics, medicine, quantum physics, brain research, and labour law. It gained a unique level of autonomy on 1 January 2008 by returning to its historic roots as a "foundation university". Today, it is one of the three largest universities in Germany. Together with the Technical University of Darmstadt and the University of Mainz, it is a partner in the inter-state strategic Rhine-Main University Alliance. Internet: http://www.goethe-universitaet.de

Publisher: The President of Goethe University Editor: Dr. Markus Bernards, Science Editor, PR & Communication Department, Theodor-W.-Adorno-Platz 1, 60323 Frankfurt am Main, Tel: -49 (0) 69 798-12498, Fax: +49 (0) 69 798-763 12531, bernards@em.uni-frankfurt.de

Publisher: The President of Goethe University Editor: Dr. Anke Sauter, Science and Humanities Editor, International Communication, PR & Communication Department, Theodor-W.-Adorno-Platz 1, 60323 Frankfurt am Main, Tel: +49(0)69 798-13066, Fax +49(0)69 798-761 12531, sauter@pvw.uni-frankfurt.de.

Goethe University Frankfurt

Related Game Theory Articles from Brightsurf:

Head in the game
Researchers at the University of Tsukuba find that blind soccer players rotate their heads downward when trapping an incoming pass.

Secrets behind "Game of Thrones" unveiled by data science and network theory
What are the secrets behind one of the most successful fantasy series of all time?

A memory game could help us understand brain injury
A Boston University team created a memory game for mice in order to examine the function of two different brain areas that process information about the sensation of touch and the memory of previous events.

Is video game addiction real?
A recent six-year study, the longest study ever done on video game addiction, found that about 90% of gamers do not play in a way that is harmful or causes negative long-term consequences.

Game theory suggests more efficient cancer therapy
Cornell mathematicians are using game theory to model how this competition could be leveraged, so cancer treatment -- which also takes a toll on the patient's body -- might be administered more sparingly, with maximized effect.

Kids eat more calories in post-game snacks than they burn during the game
A new study led by Brigham Young University public health researchers finds the number of calories kids consume from post-game snacks far exceeds the number of calories they actually burn playing in the game.

Can exercise improve video game performance?
Time spent playing video games is often seen as time stolen from physical activities.

APS tip sheet: Dark matter's galactic emissions and game theory of vaccination
The APS Tip Sheet highlights noteworthy research recently published in the Physical Review Journals.

Get your game face on: Study finds it may help
Could putting on a serious face in preparation for competition actually impact performance?

Researchers use game theory to successfully identify bacterial antibiotic resistance
Washington State University researchers have developed a novel way to identify previously unrecognized antibiotic-resistance genes in bacteria.

Read More: Game Theory News and Game Theory Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.